Gene coexpression networks inferred by correlation from high throughput profiling such as microarray data represent a simple but effective technique for discovering and interpreting linear gene relationships. In the last years several approach have been proposed to tackle the problem of deciding when the resulting correlation values are statistically significant. This is mostly crucial when the number of samples is small, yielding a non negligible chance that even high correlation values are due to random effects. Here we introduce a novel hard thresholding solution based on the assumption that a coexpression network inferred by randomly generated data is expected to be empty. The theoretical derivation of the new bound by geometrical methods is shown together with applications in onco- and neurogenomics.